A Merging Algorithm for Gaussian Mixture Components

27 Pages Posted: 15 Mar 2013

See all articles by Andrea Pastore

Andrea Pastore

Ca Foscari University of Venice - Dipartimento di Economia

Stefano Tonellato

Ca Foscari University of Venice - Dipartimento di Economia

Date Written: March 14, 2013

Abstract

In finite mixture model clustering, each component of the fitted mixture is usually associated with a cluster. In other words, each component of the mixture is interpreted as the probability distribution of the variables of interest conditionally on the membership to a given cluster. The Gaussian mixture model (GMM) is very popular in this context for its simplicity and flexibility. It may happen, however, that the components of the fitted model are not well separated. In such a circumstance, the number of clusters is often overestimated and a better clustering could be obtained by joining some subsets of the partition based on the fitted GMM. Some methods for the aggregation of mixture components have been recently proposed in the literature. In this work, we propose a hierarchical aggregation algorithm based on a generalisation of the definition of silhouette-width taking into account the Mahalanobis distances induced by the precision matrices of the components of the fitted GMM. The algorithm chooses the number of groups corresponding to the hierarchy level giving rise to the highest average-silhouette-width. Some simulation experiments and real data applications indicate that its performance is at least as good as the one of other existing methods.

Keywords: Gaussian mixtures, model based clustering, silhouette width, dissimilarity

JEL Classification: C39, C46

Suggested Citation

Pastore, Andrea and Tonellato, Stefano, A Merging Algorithm for Gaussian Mixture Components (March 14, 2013). University Ca' Foscari of Venice, Dept. of Economics Research Paper Series No. 04/WP/2013, Available at SSRN: https://ssrn.com/abstract=2233307 or http://dx.doi.org/10.2139/ssrn.2233307

Andrea Pastore (Contact Author)

Ca Foscari University of Venice - Dipartimento di Economia ( email )

Cannaregio 873
Venice, 30121
Italy

Stefano Tonellato

Ca Foscari University of Venice - Dipartimento di Economia ( email )

Cannaregio 873
Venice, 30121
Italy

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